Empirical Asset Pricing with Nonlinear Risk Premia

We introduce a new model for the joint dynamics of the S&P 100 index and the VXO implied volatility index. The nonlinear specification of the variance process is designed to simultaneously accommodate extreme persistence and strong mean reversion. This grants superior forecasting power over the standard (linear) specifications for implied variance forecasting. We obtain statistically significant predictions in an out-of-sample exercise spanning several market crashes starting 1986 and including the recent subprime crisis. The model specification is possible through a simple continuous-time no-arbitrage asset pricing framework that combines semi-analytic pricing with a nonlinear specification for the market price of risk.